The Kumaraswamy Poisson-G Family of Distribution: Its Properties and Applications

In this paper, a new family of lifetime distribution named as the Kumaraswamy Poisson-G distribution is proposed. This model is obtained by mixing the distribution of the minimum of a random number of independent identically Kumaraswamy-G distributed random variables and zero truncated Poisson random variable. The density and survival function are expressed as infinite linear mixture of the Poisson-G distribution. Some mathematical and statistical properties such as quantile function, skewness, kurtosis, probability weighted moments, moment generating function, entropy and asymptotes are investigated. Numerical computation of moments, skewness, kurtosis and entropy are tabulated for a particular distribution of the family with select parameter values. Parameter estimation by methods of maximum likelihood is discussed. Extensive simulation study is carried out under varying sample size to assess the performance of the estimation. A selected distribution from the proposed family is compared with some recently proposed ones by considering two failure time data fitting applications to justify the suitability of the proposed models.